softfloat/f16_rem.c

   1
   2 /*============================================================================
   3
   4 This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
   5 Package, Release 3d, by John R. Hauser.
   6
   7 Copyright 2011, 2012, 2013, 2014, 2015, 2016 The Regents of the University of
   8 California.  All rights reserved.
   9
  10 Redistribution and use in source and binary forms, with or without
  11 modification, are permitted provided that the following conditions are met:
  12
  13  1. Redistributions of source code must retain the above copyright notice,
  14     this list of conditions, and the following disclaimer.
  15
  16  2. Redistributions in binary form must reproduce the above copyright notice,
  17     this list of conditions, and the following disclaimer in the documentation
  18     and/or other materials provided with the distribution.
  19
  20  3. Neither the name of the University nor the names of its contributors may
  21     be used to endorse or promote products derived from this software without
  22     specific prior written permission.
  23
  24 THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
  25 EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  26 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
  27 DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
  28 DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  29 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  30 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
  31 ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  32 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  33 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  34
  35 =============================================================================*/
  36
  37 #include <stdbool.h>
  38 #include <stdint.h>
  39 #include "platform.h"
  40 #include "internals.h"
  41 #include "specialize.h"
  42 #include "softfloat.h"
  43
  44 float16_t f16_rem( float16_t a, float16_t b )
  45 {
  46     union ui16_f16 uA;
  47     uint_fast16_t uiA;
  48     bool signA;
  49     int_fast8_t expA;
  50     uint_fast16_t sigA;
  51     union ui16_f16 uB;
  52     uint_fast16_t uiB;
  53     int_fast8_t expB;
  54     uint_fast16_t sigB;
  55     struct exp8_sig16 normExpSig;
  56     uint16_t rem;
  57     int_fast8_t expDiff;
  58     uint_fast16_t q;
  59     uint32_t recip32, q32;
  60     uint16_t altRem, meanRem;
  61     bool signRem;
  62     uint_fast16_t uiZ;
  63     union ui16_f16 uZ;
  64
  65     /*------------------------------------------------------------------------
  66     *------------------------------------------------------------------------*/
  67     uA.f = a;
  68     uiA = uA.ui;
  69     signA = signF16UI( uiA );
  70     expA  = expF16UI( uiA );
  71     sigA  = fracF16UI( uiA );
  72     uB.f = b;
  73     uiB = uB.ui;
  74     expB = expF16UI( uiB );
  75     sigB = fracF16UI( uiB );
  76     /*------------------------------------------------------------------------
  77     *------------------------------------------------------------------------*/
  78     if ( expA == 0x1F ) {
  79         if ( sigA || ((expB == 0x1F) && sigB) ) goto propagateNaN;
  80         goto invalid;
  81     }
  82     if ( expB == 0x1F ) {
  83         if ( sigB ) goto propagateNaN;
  84         return a;
  85     }
  86     /*------------------------------------------------------------------------
  87     *------------------------------------------------------------------------*/
  88     if ( ! expB ) {
  89         if ( ! sigB ) goto invalid;
  90         normExpSig = softfloat_normSubnormalF16Sig( sigB );
  91         expB = normExpSig.exp;
  92         sigB = normExpSig.sig;
  93     }
  94     if ( ! expA ) {
  95         if ( ! sigA ) return a;
  96         normExpSig = softfloat_normSubnormalF16Sig( sigA );
  97         expA = normExpSig.exp;
  98         sigA = normExpSig.sig;
  99     }
 100     /*------------------------------------------------------------------------
 101     *------------------------------------------------------------------------*/
 102     rem = sigA | 0x0400;
 103     sigB |= 0x0400;
 104     expDiff = expA - expB;
 105     if ( expDiff < 1 ) {
 106         if ( expDiff < -1 ) return a;
 107         sigB <<= 3;
 108         if ( expDiff ) {
 109             rem <<= 2;
 110             q = 0;
 111         } else {
 112             rem <<= 3;
 113             q = (sigB <= rem);
 114             if ( q ) rem -= sigB;
 115         }
 116     } else {
 117         recip32 = softfloat_approxRecip32_1( (uint_fast32_t) sigB<<21 );
 118         /*--------------------------------------------------------------------
 119         | Changing the shift of `rem' here requires also changing the initial
 120         | subtraction from `expDiff'.
 121         *--------------------------------------------------------------------*/
 122         rem <<= 4;
 123         expDiff -= 31;
 124         /*--------------------------------------------------------------------
 125         | The scale of `sigB' affects how many bits are obtained during each
 126         | cycle of the loop.  Currently this is 29 bits per loop iteration,
 127         | which is believed to be the maximum possible.
 128         *--------------------------------------------------------------------*/
 129         sigB <<= 3;
 130         for (;;) {
 131             q32 = (rem * (uint_fast64_t) recip32)>>16;
 132             if ( expDiff < 0 ) break;
 133             rem = -((uint_fast16_t) q32 * sigB);
 134             expDiff -= 29;
 135         }
 136         /*--------------------------------------------------------------------
 137         | (`expDiff' cannot be less than -30 here.)
 138         *--------------------------------------------------------------------*/
 139         q32 >>= ~expDiff & 31;
 140         q = q32;
 141         rem = (rem<<(expDiff + 30)) - q * sigB;
 142     }
 143     /*------------------------------------------------------------------------
 144     *------------------------------------------------------------------------*/
 145     do {
 146         altRem = rem;
 147         ++q;
 148         rem -= sigB;
 149     } while ( ! (rem & 0x8000) );
 150     meanRem = rem + altRem;
 151     if ( (meanRem & 0x8000) || (! meanRem && (q & 1)) ) rem = altRem;
 152     signRem = signA;
 153     if ( 0x8000 <= rem ) {
 154         signRem = ! signRem;
 155         rem = -rem;
 156     }
 157     return softfloat_normRoundPackToF16( signRem, expB, rem );
 158     /*------------------------------------------------------------------------
 159     *------------------------------------------------------------------------*/
 160  propagateNaN:
 161     uiZ = softfloat_propagateNaNF16UI( uiA, uiB );
 162     goto uiZ;
 163  invalid:
 164     softfloat_raiseFlags( softfloat_flag_invalid );
 165     uiZ = defaultNaNF16UI;
 166  uiZ:
 167     uZ.ui = uiZ;
 168     return uZ.f;
 169
 170 }
 171